PUB - Publikationen an der Universität Bielefeld

Let I(n, t) be the class of all t-intersecting families of subsets of [n] and set I-k(n, t) = I(n, t) boolean AND 2(([n])(k)), I-less than or equal tok(n, t) = I(n, t) boolean AND 2(([n])(less than or equal tok)). After the maximal families in I(n, t) [13] and in I-k(n, t) [1, 9] are known we study now maximal families in I-less than or equal tok(n, t). We present a conjecture about the maximal cardinalities and prove it in several cases. More generally cardinalities are replaced by weights and asymptotic estimates are given. Analogous investigations are made for I(n, t) boolean AND C(n, s), where C(n, s) is the class of all s-cointersecting families of subsets of [n]. In particular we establish an asymptotic form of a conjecture by Bang et al. [4]. (C) 2002 Elsevier Science Ltd. All rights reserved.